1
JEE Main 2017 (Offline)
+4
-1
Let $$\omega$$ be a complex number such that 2$$\omega$$ + 1 = z where z = $$\sqrt {-3}$$. If

$$\left| {\matrix{ 1 & 1 & 1 \cr 1 & { - {\omega ^2} - 1} & {{\omega ^2}} \cr 1 & {{\omega ^2}} & {{\omega ^7}} \cr } } \right| = 3k$$,

then k is equal to :
A
z
B
-1
C
1
D
-z
2
JEE Main 2016 (Online) 9th April Morning Slot
+4
-1
The point represented by 2 + i in the Argand plane moves 1 unit eastwards, then 2 units northwards and finally from there $$2\sqrt 2$$ units in the south-westwardsdirection. Then its new position in the Argand plane is at the point represented by :
A
2 + 2i
B
1 + i
C
$$-$$1 $$-$$ i
D
$$-$$2 $$-$$2i
3
JEE Main 2016 (Offline)
+4
-1
A value of $$\theta \,$$ for which $${{2 + 3i\sin \theta \,} \over {1 - 2i\,\,\sin \,\theta \,}}$$ is purely imaginary, is :
A
$${\sin ^{ - 1}}\left( {{{\sqrt 3 } \over 4}} \right)$$
B
$${\sin ^{ - 1}}\left( {{1 \over {\sqrt 3 }}} \right)\,$$
C
$${\pi \over 3}$$
D
$${\pi \over 6}$$
4
JEE Main 2015 (Offline)
+4
-1
A complex number z is said to be unimodular if $$\,\left| z \right| = 1$$. Suppose $${z_1}$$ and $${z_2}$$ are complex numbers such that $${{{z_1} - 2{z_2}} \over {2 - {z_1}\overline {{z_2}} }}$$ is unimodular and $${z_2}$$ is not unimodular. Then the point $${z_1}$$ lies on a :
A
B
circle of radius $${\sqrt 2 }$$.
C
straight line parallel to x-axis
D
straight line parallel to y-axis.
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